Matrix Groups: An Introduction to Lie Group Theory (Springer Undergraduate Mathematics) (Paperback)

Matrix Groups: An Introduction to Lie Group Theory (Springer Undergraduate Mathematics) By Andrew Baker Cover Image
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Description


Aimed at advanced undergraduate and beginning graduate students, this book provides a first taste of the theory of Lie groups as an appetiser for a more substantial further course. Lie theoretic ideas lie at the heart of much of standard undergraduate linear algebra and exposure to them can inform or motivate the study of the latter.
The main focus is on matrix groups, i.e., closed subgroups of real and complex general linear groups. The first part studies examples and describes the classical families of simply connected compact groups. The second part introduces the idea of a lie group and studies the associated notion of a homogeneous space using orbits of smooth actions.
Throughout, the emphasis is on providing an approach that is accessible to readers equipped with a standard undergraduate toolkit of algebra and analysis. Although the formal prerequisites are kept as low level as possible, the subject matter is sophisticated and contains many of the key themes of the fully developed theory, preparing students for a more standard and abstract course in Lie theory and differential geometry.
Product Details
ISBN: 9781852334703
ISBN-10: 1852334703
Publisher: Springer
Publication Date: November 9th, 2001
Pages: 330
Language: English
Series: Springer Undergraduate Mathematics